The figure ABC is a right-angled triangle with lengths AB = AC = 4. Point A

_{1}is the mid-point of the line AC; the point A

_{2}is the mid-point of the line segment A

_{1}C, and so on. The line segment A

_{1}B

_{1}is perpendicular to AC and intersects the line BC at point B

_{1}; similarly A

_{2}B

_{2}is perpendicular to AC and intersects BC at B

_{2}, and so on.

This construction gives us the diagonal line segments of lengths BA

_{1}, B

_{1}A

_{2}, B

_{2}A

_{3}and so on. Calculate the sum of the infinite series

D = BA

_{1}+ B

_{1}A

_{2}+ B

_{2}A

_{3}+ B

_{3}A

_{4}+ ...

Hence, if H is the length BC, find the value of D/H.

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